Download Algebra I - Nashville Christian School

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2016 NCS Summer Packet Algebra 1
In order to review the basic concepts prior to taking Algebra I, the mathematics department
has prepared this review packet. The problems in this packet are designed to help you review topics from
previous mathematics courses that are important to your success in Algebra I. Because these are review
topics, you are responsible for completing the work before the first day of school. There are websites listed
on the last page, so you can look up topics if needed. This packet is required, and you need to show all your
work to receive credit. Your Algebra 1 teacher will not check for completion, but instead for accuracy. If you
use notebook paper to solve, number the pages and keep them together, then attach them to your packet.
Make sure your final answer is written in your packet.
Order of Operations
ORDER OF OPERATIONS
Key Concept
Order of Operations
Step 1
Evaluate expressions inside grouping symbols (parentheses (), brackets [ ],
braces { }, and fraction bars)
Step 2
Evaluate powers (exponents).
Step 3
Do all multiplication and/or division from left to right
Step 4
Do all addition and/or subtraction from left to right
1)
14  7 + 32
2)
42  2(-12 + 9)
5)
18 – 30 ÷ 5
6)
48 ÷ (5 + 7) – 9
3)
49
7)
4)
|-14|
43 – 5(2) + 13
Adding/Subtracting/Multiplying/Dividing Positive and Negative Numbers
Here's How:
1.
Adding Rules:
Positive + Positive = Positive: 5 + 4 = 9
Negative + Negative = Negative: (- 7) + (- 2) = - 9
Sum of a negative and a positive number:
Use the sign of the larger number and subtract
(- 7) + 4 = -3
6 + (-9) = - 3
(- 3) + 7 = 4
5 + ( -3) = 2
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2.
Subtracting Rules:
Negative - Positive = Negative: (- 5) - 3 = -5 + (-3) = -8
Positive - Negative = Positive + Positive = Positive: 5 - (-3) = 5 + 3 = 8
Negative - Negative = Negative + Positive = Use the sign of the larger number and subtract (Change double
negatives to a positive)
(-5) - (-3) = ( -5) + 3 = -2
(-3) - ( -5) = (-3) + 5 = 2
3.
Multiplying Rules:
Positive x Positive = Positive: 3 x 2 = 6
Negative x Negative = Positive: (-2) x (-8) = 16
Negative x Positive = Negative: (-3) x 4 = -12
Positive x Negative = Negative: 3 x (-4) = -12
4
3
 
10)  4 
8) -2 + 11 – 7
9) 5 – 3 + 12 – (-9)
11) (-2)(4)(-5)(-1)
12) -4 + -9 – 3(-6)
 3  7 
13)    
 5  12 
1 7

3 9
 2  5
16)    1 
3  9
14)
3 1

4 6
15) 2
Evaluating Expressions
 Substitute the given value(s) of the variable(s).
 Use order of operations to find the value of the resulting numerical expression.
Tutorials:
http://www.math.com/school/subject2/lessons/S2U2L3GL.html
http://www.purplemath.com/modules/evaluate.htm
17) 3(n – 1) + 2n, when n = 5
18) 7b – 2a, when a = -3 and b = 4
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2r
 7 , when r = 12 and t = 3
t
19) 3x2 + 5x + 1, when x = -2
20)
21) (3x)2 – 7y2, when x = 3 and y = 2
22) 4(3d + 6) – 2d, when d = -6
Solving Equations
Here is an example:
3b + 2 = 6(3 – b)
3b + 2 = 18 – 6b
-2 -2
3b = 16 – 6b
+6b
+ 6b
9b = 16
9
9
16
b=
9
Check:
16
16
Does 3( ) + 2 = 6(3 – ( ))?
9
9
16
11
+ 2 = 6( )
3
9
16 6 22
+ =
3
3
3
22 22
=
✓
3
3
Solve the equation. Include a check method to make sure you are correct.
23) 14 = b + 5
24) 5r = 22
26) 3x – 5 = 13
27)
1
d 23
4
25)
x
 9
4
28) -21 – 5x = 64
29) 3y + 2y = 81 – 6
30) 18y – 21 = 15y + 3
31)
32) 2x – 10 + 2 = 12
33) 3(y – 4) = -2y – 12
34)
2a 2

7 3
4x 6

7 5
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Properties
Match each equation on the left with the property it illustrates on the right.
35) 4 + (9 + 6) = (4 + 9) + 6
A.
Identity Property of Addition
36) x + 12 = 12 + x
B.
Associative Property
37) (3 + y) + 0 = 3 + y
C.
Distributive Property
38) x  1 = x
D.
Identity Property of Multiplication
39) 5(x + y) = 5x + 5y
E.
Commutative Property
Distributive Property
Simplify each expression using the distributive property.
Example: 4(x + 5) = 4(x) + 4(5) = 4x + 20
40) 3(b + 9)
41)
5(2x – 3)
42)
-3(4x + 9)
43) x(2x + 4)
44)
½(4r + 12)
45)
-(6p – 11)
Subsets of Real Numbers and Number Sense
46) List all the perfect squares between 1 and 250
47) What is the smallest prime number? The smallest composite number?
48) List 4 factors of 24. List 4 multiples of 24.
49) Are both 7 and –½ integers? Why or why not?
50) Are both 7 and –½ rational numbers? Why or why not?
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51) Round 43.77301 to the nearest hundredth.
52) Round -5.1982569 to the nearest hundredth.
Simplifying Expressions
Simplify each expression by distributing and combining like terms.
Algebraic expressions can be simplified like the example above by Combining Like Terms. Consider the algebraic
expression below:
12x + 7 + 5x
As you know, 12x and 5x are like terms. Therefore the coefficients, 12 and 5, can be added. This is a simple example
of Combining Like Terms.
17x + 7
53)
4x + 7y – 14x + 2y
54)
-13 – 4y – 5z + 15 – (-4z) + 11y
55)
20xy + 3x2y – 10x2y – 30xy
56)
-3(2x – 5y)
57)
9(6 + 2y) – 5 + 2y
58)
2(3x – 1) + 3(x + 7)
59)
9(2x + 4) – 2(3x – 1)
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Translating Expressions and Equations
Write an algebraic expression or equation to represent each verbal expression.
n
 18
3
7 less than fifteen times a number
Example: 18 less than the quotient of a number and 3. 
60)
The sum of six times a number and 25
61)
63)
Four times the square of a number
increased by five times the same number
64)
The sum of a number and 23 is 78.
65)
The sides of a rectangle are a number
and 4 less than that same numbers. The
perimeter is 56. Find the dimensions of
the rectangle.
66)
If a number is decreased by 6, and the
result is multiplied by 3, than the answer
is 15. Find the unknown number.
Consecutive Number Problems
Give an equation that represents the phrase. Include checks for each problem.
An integer is a – or + whole number.
67) The sum of two consecutive integers is 61.
68) The sum of three consecutive even integers
is 144.
69) Find two consecutive odd whole numbers whose sum is 2 less than 6 times the first number.
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Word Problems
Write an equation to mode each word problem. Include let statements and checks for each problem.
70) Joelle had $24 to spend on seven pencils.
After buying them she had $10. How much did
each pencil cost?
Example:
Let x = cost per pencil
7x + 10 = 24
-10 -10
7x = 14
7 7
x=2
73) 331 students went on a field trip. Six buses
were filled and 7 students traveled in cars. How
many students were in each bus?
Check:
Does 7(2) + 10 = 24?
14 + 10 = 24
24 = 24
Each pencil cost 2 dollars.
71 ) Marla bought seven boxes. A week later half
of all her boxes were destroyed in a fire.
There are now only 22 boxes left. With how
many did she start?
72) Coral spent half of her weekly allowance
playing mini-golf. To earn more money her
parents let her wash the car for $4. What is her
weekly allowance if she ended with $12?
74) You bought a magazine for $5 and four
erasers. You spent a total of $25. How much did
each eraser cost?
75) Jacki won 40 super bouncy balls playing
horseshoes at her school's game night. Later, she
gave two to each of her friends. She only has 8
remaining. How many friends does she have?
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Radicals (answers should be simplified to a whole number or it can have a root – but no decimals!)
76.
1000x 3
77.
79.
27a2
80.
82.
8 7 9 7
20xy 2
78.
3 3 9 3 4 3
83.
81.
 144a2
2 5  2 36  3 45
3 11 2 44  11
Pythagorean Theorem
84. A ladder is leaning against the side of a 10m house. If the base of the ladder is 3m away from the
house, how tall is the ladder? Round your answer to the nearest hundredth. Please draw a diagram
and show all work.
85.
A baseball diamond is a square with sides of 90 feet. What is the shortest distance, to the nearest
tenth of a foot, between first base and third base? Please draw a diagram and show all work.
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Here are some websites you might find useful in completing your summer assignment.
1.
2.
3.
4.
http://www.regentsprep.org – use the Math A site
http://www.math.com – use both Algebra and Pre-Algebra
http:// library.thinkqest.org
http://www.mathgoodies.com/lessons/toc_vol5.html – there are others on here, but this
the integer site
5. http://www.teacherschoice.com.au/Maths_Library/Algebra/Alg_1.htm
6. http://education.jlab.org/solquiz
7. http://w3.fiu.edu/math/cine_math/fast/pie.htm -- solving equations
8. http://www.algebrahelp.com/worksheets/
9. http://www.math.com/homeworkhelp/Algebra.html
10. http://www.math.com/homeworkhelp/PreAlgebra.html
11. https://www.youtube.com/user/FortBendTutoring - has great videos that explain topics well
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